Dear all,
you're invited to the seminar that will take place, in hybrid mode, at the Department of Statistics and Quantitative Methods, University of Milano-Bicocca. More details: • Speaker: Katia Colaneri (email: katia.colaneri@uniroma2.it mailto:katia.colaneri@uniroma2.it) Title: Some Optimisation Problems in Insurance with a Terminal Distribution Constraint
Abstract: In this paper, we study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time T follows a normal distribution with a given mean and a given variance. In both cases, the surplus of the insurance company is assumed to follow a Brownian motion with drift. First, we allow the insurance company to pay dividends and seek to maximise the expected discounted dividend payments or to minimise the ruin probability under the terminal distribution constraint. Here, we find explicit expressions for the optimal strategies in both cases, when the dividend strategy is updated at discrete points in time and continuously in time. Second, we let the insurance company buy a reinsurance contract for a pool of insured or a branch of business. We only allow for piecewise constant reinsurance strategies producing a normally distributed terminal surplus, whose mean and variance lead to a given Value at Risk or Expected Shortfall at some confidence level α. We investigate the question which admissible reinsurance strategy produces a smaller ruin probability, if the ruin-checks are due at discrete deterministic points in time.
This presentation is based on a joint work with Julia Eisenberg (TU Vienna) and Benedetta Salterini (University of Firenze)
Seminar venue: University of Milano-Bicocca Department of Statistics and Quantitative Methods Aula Seminari 4026, 4th floor, Building U7 January 25th, 4:30 pm Webex Link :
https://unimib.webex.com/unimib/j.php?MTID=m40cd4bb0d7bb8035ca68f3821f453b33 https://unimib.webex.com/unimib/j.php?MTID=m40cd4bb0d7bb8035ca68f3821f453b33
Join by meeting number Meeting number (access code): 2743 983 3965 Meeting password: c2uJfPBVe83 (22853728 from phones)
Best regards, Valeria
Dear all,
you're invited to the seminar that will take place, in hybrid mode, at the Department of Statistics and Quantitative Methods, University of Milano-Bicocca. More details:
Seminar Venue: University of Milano-Bicocca Department of Statistics and Quantitative Methods Seminar Room 2062, 2nd floor, Building U7
February 7th, 6:00 pm
Webex Link: https://unimib.webex.com/unimib/j.php?MTID=m0cc9dedd3361bac59dc925ac98bd4b50 https://unimib.webex.com/unimib/j.php?MTID=m0cc9dedd3361bac59dc925ac98bd4b50 Password: ytFPzwms558
Speaker: Ruodu Wang (email: ruodu.wang@uwaterloo.ca) Title: E-backtesting
Abstract: In the recent Basel Accords, the Expected Shortfall (ES) replaces the Value-at-Risk (VaR) as the standard risk measure for market risk in the banking sector, making it the most important risk measure in financial regulation. One of the most challenging tasks in risk modeling practice is to backtest ES forecasts provided by financial institutions. To design a model-free backtesting procedure for ES, we make use of the recently developed techniques of e-values and e-processes. Modelfree e-statistics are introduced to formulate e-processes for risk measure forecasts, and unique forms of model-free e-statistics for VaR and ES are characterized using recent results on identification functions. For a given model-free e-statistic, optimal ways of constructing the e-processes are studied. The proposed method can be naturally applied to many other risk measures and statistical quantities. We conduct extensive simulation studies and data analysis to illustrate the advantages of the model-free backtesting method, and compare it with the ones in the literature.
Best regards, Valeria
Dear all,
you're invited to the following seminar that will take place, in hybrid mode, at the Department of Statistics and Quantitative Methods, University of Milano-Bicocca.
Best regards, Valeria
More details:
Seminar Venue: University of Milano-Bicocca Department of Statistics and Quantitative Methods Seminar Room 4026, 4^th floor, Building U7
May 30th, 11:45 am
Webex Link: https://unimib.webex.com/unimib/j.php?MTID=m95658ae13e118ab4e8deaba9b180f0c6
Speaker: Gian Paolo Clemente (email: GianPaolo.Clemente@unicatt.it mailto:GianPaolo.Clemente@unicatt.it)
Title: Geo-referenced data and complex networks for measuring road accident risk
Abstract: Estimating the risk of motor vehicle accidents in road networks is a relevant topic for both political decisions and insurance companies. To this end, we show how the spatial objects and the information concerning the structure of the roads that can be collected, e.g. from open data sources, along with the crash history can be used to map the risk related to each road. In particular, we follow a combined approach. On the one hand, a statistical model is developed in order to assess the risk on the basis of a set of features related to the characteristics of the streets. On the other hand, from the spatial object we build a weighted network, where vertices and arcs correspond to geographical elements as junctions and roads respectively and where the assessed risk of each segment is used as a weight. We study the topology structure of the graph obtained and we show how classical network indicators can provide meaningful insights about the risk of an area. To achieve our aim, we need to adapt the current methodology about geospatial modelling to the constraints derived from the maps of the roads of a particular area and to exploit supervised/unsupervised statistical learning algorithms to estimate the local risk of the frequency of accidents (and potentially of the severity). We do not consider here other features that can be detected by telematic data or by adding other data sources (e.g., driving behaviour, driving habits, KM coverage, daytime, weather conditions, etc.). A model is developed in order to assess the risk on the basis of a set of features related to the characteristics of the roads. The spatial object and the accident risk assessed by the model for each road are then converted in a directed and weighted graph. In particular, we focus on a “junction graph", where each segment is an arc and nodes are given by junctions (or by termination of closed streets). Each arc is then weighted according to the risk of the segment detected at previous step. Focusing on network topological indicators, we observe a significant correlation between the risk associated to a node and the node betweenness measured on the network. Therefore, the centrality of a node in the topological structure appears related to the risk measured by the model. Additionally, we detect communities in the area that depend on both the arc density and the weights. The split of the area into clusters can be used by insurance companies to measure the propensity to get an accidents in the neighbour of a point, and then to fine tune the cost of premiums to be paid to drive a car. A numerical application based on Milan area in Italy (city and province) is provided.
********************************************** Valeria Bignozzi Associate Professor in Mathematical Methods for Economics, Actuarial Science and Finance Departments of Statistics and Quantitative Methods (DISMEQ), University of Milano-Bicocca, Office U7-4128 https://unimib.webex.com/meet/valeria.bignozzi
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Valeria Bignozzi